CAMGSD Seminars

We study the problem of static, spherically symmetric, self-gravitating elastic matter distributions in Newtonian gravity. To this purpose we first introduce a new definition of homogeneous, spherically symmetric (hyper)elastic body in Euler coordinates, i.e., in terms of matter fields defined on the current physical state of the body. We show that our definition is equivalent to the classical one existing in the literature and which is given in Lagrangian coordinates, i.e., in terms of the deformation of the body from a given reference state.

The analytically extended Kerr and Reissner-Nordström metrics, describing respectively spinning or spherical charged black holes (BHs), reveal a traversable passage through an inner horizon (IH) to another external universe. Consider a traveler intending to access this other universe. What will she encounter along the way? Is her mission doomed to fail? Does this other external universe actually exist?

I will explain how three integration techniques for producing cohomology classes — Chen integrals for loop spaces, Bott-Taubes integrals for knots and links, and Kontsevich integrals for configuration spaces — come together in the computation of the cohomology of spaces of braids. The relationship between various integrals is encoded by certain graph complexes. I will also talk about the generalizations to other spaces of maps into configuration spaces (of which braids are an example).

I will first recall Lusztig's asymptotic Hecke algebra and its categorification, a fusion category obtained from the perverse homology of Soergel bimodules. For example, for finite dihedral Coxeter type this fusion category is a 2-colored version of the semisimplified quotient of the module category of quantum $\operatorname{sl}(2)$ at a root of unity, which Reshetikhin-Turaev and Turaev-Viro used for the construction of 3-dimensional Topological Quantum Field Theories.

This is a report on joint work with Alex Waldron.

The Yang-Mills functional is the most studied functional on the space of connections on a vector bundle over an oriented Riemannian manifold. Its negative gradient flow leads to a semi-parabolic PDE known as the Yang-Mills flow.

In this talk I will discuss the existence of complete extremal metrics on the complement of simple normal crossings divisors in compact Kähler manifolds, and stability of pairs, in the toric case.

We explain the notion of ultragraphs, which generalize directed graphs, and use this combinatorial object to define a notion of (one-sided) edge shift spaces (which, in the finite case, coincides with the edge shift space of a graph). We then go on to show that these shift spaces have some nice properties, as for example metrizability and basis of compact open sets.

I plan to cover the following topics: Euler equations; Burger's equation; p-system; symmetric hyperbolic PDE's; shock formation; Lax method of solving Riemann problems; Glimm's method for solving Cauchy problems; Entropy solutions; artificial viscosity.

I plan to cover the following topics: Euler equations; Burger's equation; p-system; symmetric hyperbolic PDE's; shock formation; Lax method of solving Riemann problems; Glimm's method for solving Cauchy problems; Entropy solutions; artificial viscosity.